Israeli prime minister Benjamin Netanyahu has ordered the defence forces to prepare for the possibility of a "significant widening" of the ground invasion into Gaza.

After 10 days of cross-border violence between the Jewish state and militants in the Palestinian enclave, Israeli infantry and tanks crossed into Gaza on Thursday night (local time).

Soldiers have been seeking out tunnels dug by Palestinian militants underneath the border into Israel, and more than a dozen have been discovered and destroyed.

Mr Netanyahu met with his security cabinet overnight and has warned that he is ready to expand the invasion.

"We chose to start this operation after we exhausted other options and reached the conclusion that without it we could pay a much higher price," he said.

"The main goal is to restore quiet. My instructions ... to the Israeli army, with the approval of the security cabinet, is to prepare for the possibility of a widening, a significant widening of the ground operation."

He did not say what form a broadened offensive might take.

The Israeli troops have also been involved in firefights with Palestinian militants.

Palestinian officials say 58 Palestinians have been killed since the ground offensive began on Thursday (local time), while hundreds have been wounded.

One Israeli soldier was killed in an apparent friendly-fire incident, the military said, and several other troops were wounded in the ground operations.

As the death toll in Gaza climbs, more rockets were fired at major Israeli cities overnight.

More troops along Gaza border prepare to join attack

Thousands of troops are stationed along the border, preparing to enter Gaza to join the attack.

To back up regular forces, Israel said it was calling up 18,000 military reservists to add to the 30,000 already mobilised.

Hamas spokesman Abu Ubaida said it had thousands of fighters of its own "waiting to join the battle".

Israel has been cautioned by its main ally, the United States, about the risks of further escalation as Palestinian civilian deaths mounted.

US president Barack Obama said he had spoken to Mr Netanyahu, underscoring Washington's support for Israel to defend itself but raising concerns about "the risks of further escalation" and additional loss of innocent lives.

"We are hopeful that Israel will continue to approach this process in a way that minimises civilian casualties," Mr Obama said.

Israel launched air strikes and artillery attacks against targets in Gaza 10 days ago in response to rocket fire from Hamas militants inside the coastal enclave.

In all, 291 Palestinians - most of them civilians, of whom at least 50 were under the age of 18 - have been killed since fighting began on July 8, Gaza officials said.

There have been two Israeli fatalities - the soldier and a civilian, who was killed by a rocket.

UN Secretary-General Ban Ki-moon plans to travel to the Middle East over the weekend in a bid to end the hostilities.

The number of people in Gaza seeking sanctuary has nearly doubled since the ground offensive began.

Relief workers say there are now more than 40,000 people being protected in 34 UN shelters in the territory.

The UN says Israel has legitimate security concerns and it condemns the rocket fire from Gaza that ended a temporary ceasefire.